DISCOVER

# How to Do a Short Division Sum

Updated July 19, 2017

Division is finding out how many times one number contains another number. For example, if we divide eight by two we find out that that the number eight contains exactly four 2s. So, if we have to share eight apples among two people, each person will get four apples. If we divide eight by three we find that the number eight contains two 3s, and we have two left over as a remainder. In short division the intermediate steps are most often not written down.

Draw a box. Write the number to be divided (dividend) inside the box and the divisor (the number which will divide) outside the box. The answer (quotient) goes on top of the line.

Let us take, as an example, 842/2. So 842 is the dividend and 2 is the divisor. We want to find out how many twos there are in 842.

We look at the first number in the dividend which is 8. There are four 2s in 8, so we put 4 as the first digit in the quotient.

The next digit is 4. There are two 2s in 4, so 2 is the next digit in the quotient.

The last digit is 2. Two contains itself one time, so we write 1 as the last digit. Reading the answer from left to right, the quotient is 421. There are 421 twos in the number 842.

Let us now take as an example a number that will give a remainder. We will divide 92 by 3.

We look at the first digit in the dividend, which is 9. 3 goes into 9 three times, so we put 3 as the first digit in the quotient.

The next digit is 2. 2 does not contain any 3s because it is smaller than 3. Every digit in the dividend needs a digit in the quotient. So we put 0 as the next digit in the quotient. 2 becomes the remainder. Our quotient (answer) is 30 with a remainder 2. We can write it as 30R 2, or 30 2/3.

As another example let us divide 515 by 5. The first digit in the dividend is 5. 5 goes into 5 once, so we write 1 in the quotient.

The next digit is 1. 1 is smaller than 5, so we write 0 in the quotient above the 1, and write the 1 to the left of the next digit. So now we have 15. 5 goes into 15 exactly three times with no remainder. We write 3 above the 5. Our quotient is 103.

Let us take the number 56/5. The first digit is 5. 5 goes into 5 once, so we write 1 as the first digit in the quotient.

The next digit is 6. 5 times 1 is 5, so 5 goes into 6 once. Write 1 as the next digit in the quotient. Subtract the 5 from 6. There is 1 left over.

Instead of stopping here and writing our quotient as 11R 1, let us go on to write our answer as a decimal. So, if we come to the end of the number to be divided (dividend) and there is a remainder, we put a decimal point at the end of the dividend and add a 0 after the decimal point. And, very important, we put a decimal point in the quotient.

So we put a decimal point after 6, and then add a 0. Our number now reads 56.0

We carry the 1 remainder to the 0 to make it 10. 5 goes into 10 exactly 2 times with no remainder. We write a 2 as the next digit in the quotient, next to the decimal point. The quotient (answer) is 11.2

#### Tip

Once you have put a decimal point in the dividend you can add zeros to whatever degree of precision you like.

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